System and method for tomographic reconstruction utilizing circular trajectory and scanogram to reduce artifacts

ABSTRACT

A computed tomography apparatus and method using line data estimated from circle data and scanogram data. An image of a subject is reconstructed using the circle data and the estimated line data. The circle data and scanogram data may be weighted in estimating the line data. The apparatus and method are useful in diminishing or eliminating streak artifacts in reconstructed images such as images including the spine.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to computed tomographic (CT) imaging, andin particular to CT imaging using scanograms to estimate line data fromcircular scans.

2. Discussion of the Background

In three-dimensional (3D) cone-beam computed tomography, the circularscan is widely used because of its convenience. It is well known thatthe projection data acquired from a cone-beam circular scan are notsufficient for volumetric reconstruction. The so-called cone-beamartifacts are found in the reconstructed images from circle-onlycone-beam scan data. The low frequency shadow artifacts can be reducedby interpolation in the radon space. The high frequency artifacts due tothe longitudinal abrupt change in the imaged subject are difficult tohandle. A typical high frequency cone-beam artifact is the streaks offspines.

To eliminate the cone beam artifacts in circular cone-beam scans, anadditional line scan, arc scan, or helical scan is usually performed tomake the data complete for the volumetric reconstruction. The additionalscan may increase the complexity of the scan protocol and increase thescan time and radiation dose.

SUMMARY OF THE INVENTION

An embodiment of the apparatus according to the invention may include anx-ray source, an x-ray detector disposed to receive x-rays from thex-ray source, a unit to collect circle data and scanogram data, and aprocessing unit for estimating line data from the circle data and thescanogram data and for performing reconstruction of an image using thecircle data and the estimated line data.

An embodiment of the method according to the invention may includeexposing a subject to x-rays, collecting circle data, collectingscanogram data, estimating line data using the circle data and thescanogram data, and reconstructing an image of the subject using theestimated line data and the circle data.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the invention and many of the attendantadvantages thereof will be readily obtained as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying drawings, wherein:

FIG. 1 is a diagram of a system according to the invention;

FIG. 2 is a diagram of the geometry for the circle scans and scanogram;

FIGS. 3A and 3B are diagrams illustrating estimating data line rays;

FIG. 4 is a diagram illustrating estimating data line rays usingcomplementary data line rays;

FIG. 5 is an image of estimating line data using multiple scanogramrays;

FIG. 6 is an image of estimated line data;

FIG. 7 is a diagram illustrating a weighting factor used in the methodaccording to the invention;

FIG. 8A is a reconstructed image above the middle plane from circle dataonly;

FIG. 8B is a reconstructed image above the middle plane from circle dataand estimated line data;

FIG. 8C is a reconstructed image above the middle plane from circle dataand estimated line data with weighting;

FIG. 9 shows reconstructed images from the locally smoothed projectionsof measured circle and estimated line data;

FIG. 10 shows reconstructed images of a sagittal slice for real circleand line data (top), real circle data and estimated line data (middle)and circle data only (bottom);

FIGS. 11A-D are chest images prepared with circle data only, circle andline data, circle and scanogram data with local smoothing, and circleand scanogram data and adaptive z-filtering, respectively;

FIGS. 12A-D are abdomen images prepared with circle data only, circleand line data, circle and scanogram data with local smoothing, andcircle and scanogram data and adaptive z-filtering, respectively;

FIGS. 13A-C are chest images are reconstructed using filteredbackprojection (top images) and BPF (bottom images); and

FIGS. 14A-C are abdomen images reconstructed using filteredbackprojection (top images) and BPF (bottom images).

DETAILED DESCRIPTION

FIG. 1 shows an x-ray computed topographic imaging device according tothe present invention. The projection data measurement systemconstituted by gantry 1 accommodates an x-ray source 3 that generates acone-beam of x-ray flux approximately cone-shaped, and a two-dimensionalarray type x-ray detector 5 consisting of a plurality of detectorelements arranged in two-dimensional fashion, i.e., a plurality ofelements arranged in one dimension stacked in a plurality of rows. X-raysource 3 and two-dimensional array type x-ray detector 5 are installedon a rotating ring 2 in facing opposite sides of a subject, who is laidon a sliding sheet of a bed 6. Two-dimensional array type x-ray detector5 is mounted on rotating ring 2. Each detector element will correspondwith one channel. X-rays from x-ray source 3 are directed on to subjectthrough an x-ray filter 4. X-rays that have passed through the subjectare detected as an electrical signal by two-dimensional array type x-raydetector 5.

X-ray controller 8 supplies a trigger signal to high voltage generator7. High voltage generator 7 applies high voltage to x-ray source 3 withthe timing with which the trigger signal is received. This causes x-raysto be emitted from x-ray source 3. Gantry/bed controller 9 synchronouslycontrols the revolution of rotating ring 2 of gantry 1 and the slidingof the sliding sheet of bed 6. System controller 10 constitutes thecontrol center of the entire system and controls x-ray controller 8 andgantry/bed controller 9 and x-rays are emitted continuously orintermittently at fixed angular intervals from x-ray source 3.

The output signal of two-dimensional array type x-ray detector 5 isamplified by a data collection unit 11 for each channel and converted toa digital signal, to produce projection data. The projection data thatis output from data collection unit 11 is fed to processing unit 12.Processing unit 12 performs various processing using the projectiondata. Unit 12 performs line data estimation (as described in more detailbelow, filtering, backprojection and reconstruction. Unit 12 determinesbackprojection data reflecting the x-ray absorption in each voxel. Inthe circular scanning system using a cone-beam of x-rays as in the firstembodiment, the imaging region (effective field of view) is ofcylindrical shape of radius R centered on the axis of revolution. Unit12 defines a plurality of voxels (three-dimensional pixels) in thisimaging region, and finds the backprojection data for each voxel. Thethree-dimensional image data or tomographic image data compiled by usingthis backprojection data is sent to display device 14, where it isdisplayed visually as a three-dimensional image or tomographic image.

Circle data is obtained by circular (helical) scans of the x-ray source.The line data for reconstruction is estimated from the circle data usingthe scanogram. A scanogram is an image obtained by moving the patientthrough the CT gantry through the plane of the x-ray source anddetectors while x-ray projection measurements are made at a fixed sourceangular position. The image which is obtained in this manner is similarin general appearance to a conventional projection radiography image.Note that the scanogram is obtained with a very narrow cone beam, thatis, only a few (in the order of 2 to 4) detector rows are utilized. Onthe other hand, circular data or true line data is collected with wide(full) cone angle, when up to several hundred detector rows may beutilized. Note that for exact reconstruction both circular and line dataare necessary. An advantage of this invention is to avoid the line scan;instead, the unmeasured line data are estimated using available circleand scanogram data. Note that scanogram data is almost always availablein clinical scans because it is applied before the patient scan forpatient positioning.

FIG. 2 illustrates the geometry. Circle data and the scanogram areobtained. The circle data can be parameterized as P_(C)(u, v, λ), where(u, v) are coordinates on the detector and λ indicates the view (sourcerotation, projection) angle. Here v is the vertical detector coordinateand u is the horizontal detector coordinate; on the flat detector axis uis given by a straight line with equi-spaced linear grid; on thecylindrical detector axis u represents fan beam angle and is given bythe equiangular grid. Source to detector distance is denoted SDD, or R.The line data P_(L)(u, v, h) can be parameterized by detectorcoordinates, (u, v), and the virtual (estimated) line source position,h. Only the case where h>0 is described. However, the case where h<0 istreated likewise. Note that h<2W, where W is the detector half-width.The line data can be estimated as a weighted sum of circle data and thescanogram:

$\begin{matrix}{{P_{L}\left( {u,v,h} \right)} = {{\frac{v}{v + h}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} + {\frac{h}{v + h}{P_{S}\left( {u,{v + h}} \right)}}}} & (1)\end{matrix}$

where P_(S)(u, z) indicates the scanogram, and

₀ is the angular position at which line is attached to the circle. Forv>0 and v<0, Eq. (1) represents a linear interpolation andextrapolation, respectively.

In general, there are two different cases to estimate the ray (u, v) ofthe line data at h, depending on whether v>0 or v<0, illustrated byFIGS. 3A and 3B, respectively. The ray r_(L) is the unmeasured line dataray (γ, v) that is to be estimated. Rays, r_(C) and r_(S), are themeasured rays from the circle and scanogram data, respectively. In FIG.3A the measured rays are chosen in such way that they intersect theunmeasured ray at the virtual detector plane. Note that the ray r_(C) isgiven by (γ, v), where z=h+v, and r_(S) is given by the source positionz and fan angle γ

Turning to the case illustrated in FIG. 3B, it can be seen from thefigure that the ray r_(L) cannot be interpolated between rays r_(C) andr_(S). (The ray r_(C) is not close to r_(L)).

Therefore, the complementary circle ray r_(CC) is used, and isillustrated in FIG. 4. The source position for r_(CC) is

=

₀+;−2ε, where

₀ is the line angular position. Ray r_(CC) is chosen in such way that itintersects r_(L) midway between

and

₀.

$\begin{matrix}{{P_{L}\left( {u,v,h} \right)} = \left\{ \begin{matrix}{{w_{1}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} +} & {{{if}\mspace{14mu} v} > 0} \\{{\left( {1 - w_{1}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \; \\{{w_{2}{P_{C}\begin{pmatrix}{{- u},{v^{\prime} + h},} \\{\lambda_{0} + \pi - {2\; \gamma}}\end{pmatrix}}} +} & {{{if}\mspace{14mu} v} < 0} \\{{\left( {1 - w_{2}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \;\end{matrix} \right.} & (2) \\{where} & \; \\{w_{1} = {\frac{v}{v + h}\mspace{14mu} {for}\mspace{14mu} {both}\mspace{14mu} {cylindrical}\mspace{14mu} {and}\mspace{14mu} {flat}\mspace{14mu} {detectors}}} & (3) \\{w_{2} = {{- \frac{2v\; \cos \; u}{h}}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {cylindrical}\mspace{14mu} {detector}}} & \left( {4A} \right) \\{w_{2} = {{- \frac{2v}{h}}\frac{{SDD}^{2}}{{SDD}^{2} + u^{2}}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {flat}\mspace{14mu} {detector}}} & \left( {4B} \right) \\{v^{\prime} = {\frac{v}{\cos^{2}u}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {cylindrical}\mspace{14mu} {detector}}} & \left( {5A} \right) \\{v^{\prime} = {v\sqrt{\frac{{SDD}^{2} + u^{2}}{{SDD}^{2}}}\mspace{14mu} {for}\mspace{14mu} {the}\mspace{14mu} {flat}\mspace{14mu} {detector}}} & \left( {5B} \right)\end{matrix}$

Note that equations (3)-(4) represent linear weighting between circledata and scanogram. In general, other weights are also possible. Forexample, the following polynomial weighting may be used:

w _(1S)=3w ₁ ²−2w ₁ ³.

w _(2S)=3w ₂ ²−2w ₂ ³.

In the main embodiment, only one scanogram ray is used in the weightedsum (1) or (2). Alternatively, a plurality of scanogram rays can be usedto estimate each missing line ray, as shown in FIG. 5.

Once line data is estimated using the proposed method, any suitablereconstruction algorithm can be used. There two classes of suitablealgorithms: filtered-backprojection (FBP) and derivative backprojectionfiltration (BPF). Example of an FBP algorithm is Katsevich line+circlealgorithm (A. Katsevich, Image reconstruction for the circle and linetrajectory, Physics in Medicine and Biology, vol. 49, pp. 5059-5072,2004.) Another example of FBP algorithm that can be applied to circulardata only is Feldkamp-type reconstruction (L. A. Feldkamp, L. C. Davisand J. W. Kress, Practical cone beam algorithm, Journal of OpticalSociety of America, vol. 1 (6), pp. 612-619, June 1984.)

Also, reconstruction algorithms may use full revolution of circular data(full scan, or 1PI mode), or partial revolution (short, or half scan, or2PI mode). Both types can be used with the proposed invention.

FIG. 6 illustrates the estimated line data at one view. A chest phantomis exposed to x-ray to produce projection data. The bright lineindicates the projection of the circular trajectory. Only the data abovethe line contribute to the reconstruction. The data below the line looknoisy but do not affect the reconstructed images.

Empirical Weighting Factor

The method according to the invention is particularly useful in reducingstreak artifacts. The streak artifacts off the spine are caused by thehigh frequency components near the joints in the circle data. The highfrequency components can be compensated by line data in exactcircle-line algorithms and the streak artifacts can be avoided. FIG. 7show x-rays 16 along trajectory 15 passing through the spine 17. Thejoint close to the middle plane yields more high frequency data than thejoints far from the middle plane.

On the other hand, in the line data each joint is equivalent in thesense of high frequency components. These features for the circle dataand the line data imply that the high frequency components in the linedata related to the joint close to the middle plane tend to compensatetheir counterparts in the circle data. The high frequency components inthe line data related to the joints far from the middle plane have notheir counterparts in the circle data. Therefore they must cancel eachother within the line data. The estimated data from the scanogram andthe circle data do contain errors, especially in the high frequencycomponents. It may result in additional streak artifacts near the jointfar from the middle plane.

A weighting factor can be introduced to improve the reconstructed imagesby reducing such streaks. An empirical weighting factor

$\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right)$

is introduced to Eq. (1) or (2) to reduce the artifact:

$\begin{matrix}{{P_{LF}\left( {u,v,h} \right)} = {\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right) \times {P_{L}\left( {u,v,h} \right)}}} & (6)\end{matrix}$

where d is an adjustable parameter. The factor reduces the contributionof the line data away from the middle plane. The parameter d isdetermined empirically and ranges from 1 to 100.

FIG. 8 shows the effect of empirical weighting factor. FIG. 8A shows aslice of image above middle plane reconstructed from only the circledata. It can be seen that strong streak artifacts appear off the jointclose to middle plane (at bottom of the image) and less streaks can beseen near the joint far from the middle plane. As shown in FIG. 8B, thestreak artifacts close to the middle plane are reduced by use of theestimated line data from the scanogram but more and intense streaksappear off the second joint from the middle plane that are caused by theerrors in the estimated line data. FIG. 8C shows the reconstructed imagewith the empirical weighting factor. The streak artifacts are reducedsignificantly but some of them are still visible.

Local Smoothing

As the streak artifacts off spines are caused by the high frequencycomponents in the projection data near spine joints, the artifacts maybe also reduced by eliminating the high frequency components. A simplemethod to reduce the high frequency components is running average. Theaverage is performed only vertically and in the vicinity of spines, andis called local smoothing. FIG. 9 shows the reconstructed images fromthe locally smoothed projections of measured circle and estimated linedata. Three tests were performed with running average pixel numbers of9, 5, and 3, as an example; other values are also acceptable. The streakartifacts in the reconstructed images are reduced significantly. Thereis some blurring in the spine region. On the image with 9-pixel runningaverage (top), a bright spot and a dark spot indicated by the circles 18and 19, respectively, can be observed. On the image with 5-pixel runningaverage (middle), a dark band (arrow 20) and a dark spot 21 are visible.On the image with 3-pixel running average, a dark band and a few streaksare marked with arrows but are dimly visible. Overall, for this type ofimage the 5-pixel running average produces the best quality image.

To examine the image quality in the volume, images were reconstructed inboth upper and lower portions of the circle trajectory using the methodaccording to the invention with local smoothing. FIG. 10 shows theimages on the median plane. The quality of images from real circle andline data (top) and from real circle and estimated line data (middle) iscomparable. They are much better than that from circle-only data(bottom).

In a further modification, adaptive z-filtering is used instead of thelocal smoothing. Here the strength of smoothing in the z-direction isadapted to the data z-gradient, that is, for structures with sharperz-gradient more smoothing is applied, and vice versa. Chest regionimages comparing the adaptive z-filtering and local smoothing are shownin FIGS. 11A-D. FIG. 11A is an image reconstructed using only the circledata, while FIG. 11B is an image reconstructed using circle and linedata. FIG. 11C is an image reconstructed using the circle and scanogramdata and local smoothing as described above. FIG. 11D is an imagereconstructed using the circle and scanogram data and adaptivez-filtering. Strong and weak streak artifacts can be seen at the firstand second joints in the circle-only image (FIG. 11A). In thecircle-line image (FIG. 11B), the strong streaks are reducedsignificantly and the weak streaks disappear. The two imagesreconstructed according to the invention (FIGS. 11C-D) using the circleand scanogram data appear similar. The strong streaks are reduced andthe weak streaks disappear. Compared with that of the circle-line, thereis only a small amount of blurring. The images reconstructed accordingto the invention are good quality.

Similar results are found for abdomen images. FIGS. 12A-D illustrateimages reconstructed using only circle data, circle and line data,circle and scanogram data using local smoothing according to theinvention, and circle and scanogram data using adaptive z-filteringaccording to the invention. Strong streak artifacts can be seen at thefirst and fourth joints in the circle-only image (FIG. 12A) and the weakstreaks appear near the third joint. In the circle-line image (FIG.12B), the strong streaks are reduced and the weak streaks disappear. Thetwo images using the circle and scanogram data (FIGS. 12C-D) appearsimilar. The strong streaks are reduced and the weak streaks disappear.Compared with that of the circle-line (FIG. 12B), there is only a smallamount of blurring. Again, good quality images can be reconstructed.

A comparison of two reconstruction techniques was made. Referring toFIGS. 13A-C and 14A-C, chest and abdomen images are reconstructed usingfiltered backprojection (FBP) (top images) and backprojection-filtration(BPF) (bottom images). For the chest images, in the circle-only images(FIG. 13A), the streak artifacts from BPF are stronger than that fromFBP. For the chest images using circle-scanogram data (FIG. 13B) andcircle-line data (FIG. 13C), the images of FBP appear to be of slightlybetter quality than those of BPF. Note that the reconstruction of BPFdid not include data corrections and only use short-scan circle data.

Similar results are obtained for the abdomen images. In the circle-onlyimages (FIG. 14A), the streak artifacts from BPF are stronger than thatfrom FBP. For the abdomen images using circle-scanogram data (FIG. 14B)and circle-line data (FIG. 14C), the images of FBP appear to be ofslightly higher quality than those of BPF. Again, Note that thereconstruction of BPF did not include data corrections and only useshort scan circle data

The present invention may be implemented in software or in hardware. Inparticular the operation of the processing unit described above can becarried out as a software program run on a microprocessor or a computer.The software can be stored on a computer-readable medium and loaded intothe system.

Numerous other modifications and variations of the present invention arepossible in light of the above teachings. It is therefore to beunderstood that within the scope of the appended claims, the inventionmay be practiced otherwise than as specifically described herein.

1. A computed-tomography apparatus, comprising: an x-ray source; anx-ray detector disposed to receive x-rays from said x-ray source; a unitto collect circle data and scanogram data; a processing unit forestimating line data from said circle data and said scanogram data andfor performing reconstruction of an image using said circle data andsaid estimated line data.
 2. An apparatus as recited in claim 1, whereinsaid processing unit is configured to estimated said line data using:${P_{L}\left( {u,v,h} \right)} = {{\frac{v}{v + h}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} + {\frac{h}{v + h}{P_{S}\left( {u,{v + h}} \right)}}}$where P_(C)(u, v, λ) is said circle data and P_(S)(u, z) is saidscanogram data.
 3. An apparatus as recited in claim 1, wherein saidprocessing unit is configured to estimated said line data using:${P_{L}\left( {u,v,h} \right)} = \left\{ {{{\begin{matrix}{{w_{1}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} +} & {{{if}\mspace{14mu} v} > 0} \\{{\left( {1 - w_{1}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \; \\{{w_{2}{P_{C}\begin{pmatrix}{{- u},{v^{\prime} + h},} \\{\lambda_{0} + \pi - {2\; \gamma}}\end{pmatrix}}} +} & {{{if}\mspace{14mu} v} < 0} \\{{\left( {1 - w_{2}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \;\end{matrix}w_{1}} = {{\frac{v}{v + h}w_{2}} = {- \frac{2v\; \cos \; u}{h}}}},{{\begin{matrix}{v^{\prime} = \frac{v}{\cos^{2}u}} & {{for}\mspace{14mu} a\mspace{14mu} {cylindrical}\mspace{14mu} {detector}}\end{matrix}w_{2}} = {{- \frac{2v}{h}}\frac{{SDD}^{2}}{{SDD}^{2} + u^{2}}}},{v^{\prime} = {v\sqrt{\frac{{SDD}^{2} + u^{2}}{{SDD}^{2}}}\mspace{14mu} {for}\mspace{14mu} a\mspace{14mu} {flat}\mspace{14mu} {detector}}}} \right.$where P_(C)(u, v, λ) is said circle data, P_(S)(u, z) is said scanogramdata, and w₁ and w₂ are weighting factors.
 4. An apparatus as recited inclaim 2, wherein said processing unit is further configured to estimatesaid line data using${P_{LF}\left( {u,v,h} \right)} = {\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right) \times {P_{L}\left( {u,v,h} \right)}}$5. An apparatus as recited in claim 3, wherein said processing unit isfurther configured to estimate said line data using${P_{LF}\left( {u,v,h} \right)} = {\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right) \times {P_{L}\left( {u,v,h} \right)}}$6. An apparatus as recited in claim 3, wherein said weighting factorscomprise:w _(1S)=3w ₁ ²−2w ₁ ³.w _(2S)=3w ₂ ²−2w ₂ ³.
 7. An apparatus as recited in claim 1, whereinsaid processing unit is configured to estimate said line data usingmultiple scanogram rays for each estimated line ray.
 8. An apparatus asrecited in claim 1, wherein said processing unit is configured toestimate said line data using one of local smoothing and adaptivefiltering.
 9. An apparatus as recited in claim 1, wherein saidprocessing unit is configured to reconstruct said image using one offiltered backprojection type reconstruction and backprojectionfiltration type reconstruction.
 10. An apparatus as recited in claim 1,wherein said processing unit is configured to reconstruct said imageusing full revolution circular data.
 11. An apparatus as recited inclaim 1, wherein said processing unit is configured to reconstruct saidimage using partial revolution circular data.
 12. A computed tomographymethod, comprising: exposing a subject to x-rays; collecting circledata; collecting scanogram data; estimating line data using said circledata and said scanogram data; and reconstructing an image of saidsubject using said estimated line data and said circle data.
 13. Amethod as recited in claim 12, comprising estimating said line datausing:${P_{L}\left( {u,v,h} \right)} = {{\frac{v}{v + h}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} + {\frac{h}{v + h}{P_{S}\left( {u,{v + h}} \right)}}}$where P_(C)(u, v, λ) is said circle data and P_(S)(u, z) is saidscanogram data.
 14. A method as recited in claim 12, comprisingestimating said line data using:${P_{L}\left( {u,v,h} \right)} = \left\{ {{{\begin{matrix}{{w_{1}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} +} & {{{if}\mspace{14mu} v} > 0} \\{{\left( {1 - w_{1}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \; \\{{w_{2}{P_{C}\begin{pmatrix}{{- u},{v^{\prime} + h},} \\{\lambda_{0} + \pi - {2\; \gamma}}\end{pmatrix}}} +} & {{{if}\mspace{14mu} v} < 0} \\{{\left( {1 - w_{2}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \;\end{matrix}w_{1}} = {{\frac{v}{v + h}w_{2}} = {- \frac{2v\; \cos \; u}{h}}}},{{\begin{matrix}{v^{\prime} = \frac{v}{\cos^{2}u}} & {{for}\mspace{14mu} a\mspace{14mu} {cylindrical}\mspace{14mu} {detector}}\end{matrix}w_{2}} = {{- \frac{2v}{h}}\frac{{SDD}^{2}}{{SDD}^{2} + u^{2}}}},{v^{\prime} = {v\sqrt{\frac{{SDD}^{2} + u^{2}}{{SDD}^{2}}}\mspace{14mu} {for}\mspace{14mu} a\mspace{14mu} {flat}\mspace{14mu} {detector}}}} \right.$where P_(C)(u, v, λ) is said circle data, P_(S)(u, z) is said scanogramdata, w₁ and w₂ are weighting factors.
 15. A method as recited in claim12, comprising estimating said line data using${P_{LF}\left( {u,v,h} \right)} = {\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right) \times {P_{L}\left( {u,v,h} \right)}}$16. A method as recited in claim 14, comprising estimating said linedata using${P_{LF}\left( {u,v,h} \right)} = {\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right) \times {P_{L}\left( {u,v,h} \right)}}$17. An method as recited in claim 14, wherein said weighting factorscomprisew _(1S)=3w ₁ ²−2w ₁ ³.w _(2S)=3w ₂ ²−2w ₂ ³.
 18. A method as recited in claim 12, comprisingestimating said line data using multiple scanogram rays for eachestimated line ray.
 19. A method as recited in claim 12, comprisingestimating said line data using one of local smoothing and adaptivefiltering.
 20. A method as recited in claim 12, wherein saidreconstructing comprises one of filtered backprojection typereconstruction and backprojection filtration type reconstruction.
 21. Amethod as recited in claim 12, wherein said reconstructing comprisesreconstruction of full revolution circular data.
 22. A method as recitedin claim 12, wherein said reconstructing comprises reconstruction ofpartial revolution circular data.
 23. A computer readable-mediumcontaining instructions that may be executed by a computer to perform amethod, comprising: collecting circle data from an x-ray scan of asubject; collecting scanogram data from said x-ray scan; estimating linedata using said circle data and said scanogram data; and reconstructingan image of said subject using said estimated line data and said circledata.
 24. A medium as recited in claim 23, wherein method comprises:estimating said line data using:${P_{L}\left( {u,v,h} \right)} = {{\frac{v}{v + h}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} + {\frac{h}{v + h}{P_{S}\left( {u,{v + h}} \right)}}}$where P_(C)(u, v, λ) is said circle data and P_(S)(u, z) is saidscanogram data.
 25. A medium as recited in claim 23, wherein said methodcomprises: estimating said line data using:$\mspace{79mu} {{P_{L}\left( {u,v,h} \right)} = \left\{ {{{\begin{matrix}{{w_{1}{P_{C}\left( {u,{v + h},\lambda_{0}} \right)}} +} & {{{if}\mspace{14mu} v} > 0} \\{{\left( {1 - w_{1}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \; \\{{w_{2}{P_{C}\begin{pmatrix}{{- u},{v^{\prime} + h},} \\{\lambda_{0} + \pi - {2\; \gamma}}\end{pmatrix}}} +} & {{{if}\mspace{14mu} v} < 0} \\{{\left( {1 - w_{2}} \right){P_{S}\left( {u,{v + h}} \right)}},} & \;\end{matrix}\mspace{79mu} w_{1}} = {{\frac{v}{v + h}w_{2}} = {- \frac{2v\; \cos \; u}{h}}}},{{\begin{matrix}{v^{\prime} = \frac{v}{\cos^{2}u}} & {{for}\mspace{14mu} a\mspace{14mu} {cylindrical}\mspace{14mu} x\text{-}{ray}\mspace{14mu} {detector}}\end{matrix}w_{2}} = {{- \frac{2v}{h}}\frac{{SDD}^{2}}{{SDD}^{2} + u^{2}}}},{v^{\prime} = {v\sqrt{\frac{{SDD}^{2} + u^{2}}{{SDD}^{2}}}\mspace{14mu} {for}\mspace{14mu} a\mspace{14mu} {flat}\mspace{14mu} x\text{-}{ray}\mspace{14mu} {detector}}}} \right.}$where P_(C)(u, v, λ) is said circle data, P_(S)(u, z) is said scanogramdata, w₁ and w₂ are weighting factors.
 26. A medium as recited in claim25, wherein said method comprises: estimating said line data using${P_{LF}\left( {u,v,h} \right)} = {\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right) \times {P_{L}\left( {u,v,h} \right)}}$27. A medium as recited in claim 24, wherein said method comprises:estimating said line data using${P_{LF}\left( {u,v,h} \right)} = {\frac{1}{2}\left( {1 + {\cos \frac{h\; \pi}{d}}} \right) \times {P_{L}\left( {u,v,h} \right)}}$28. A medium as recited in claim 25, wherein said weighting factorscomprisew _(1S)=3w ₁ ²−2w ₁ ³.w _(2S)=3w ₂ ²−2w ₂ ³.
 29. A medium as recited in claim 23, wherein saidmethod comprises estimating said line data using multiple scanogram raysfor each estimated line ray.
 30. A medium as recited in claim 23,wherein said method comprises estimating said line data using one oflocal smoothing and adaptive filtering.
 31. A medium as recited in claim23, wherein said reconstructing comprises one of filtered backprojectiontype reconstruction and backprojection filtration type reconstruction.32. A medium as recited in claim 23, wherein said reconstructingcomprises reconstruction of full revolution circular data.
 33. A mediumas recited in claim 23, wherein said reconstructing comprisesreconstruction of partial revolution circular data.